This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — Here are the solutions to the questions: a) The amount of money available for Medication. Step 1: Determine the total ratio parts. The ratio for feeds, medication, and water supply is 5:3:2. Total ratio parts = 5 + 3 + 2 = 10. Step 2: Calculate the fraction of money allocated for medication. Medication corresponds to 3 parts of the ratio. Fraction for medication = (3)/(10). Step 3: Calculate the amount of money for medication. Total money = Shs. 800,000. Amount for medication = (3)/(10) × 800,000. = 3 × 80,000 = 240,000 The amount of money available for Medication is Shs. 240,000. b) How much he will pay for feeds in the third installment. Step 1: Calculate the total money allocated for feeds. Feeds correspond to 5 parts of the ratio. Fraction for feeds = (5)/(10) = (1)/(2). Amount for feeds = (1)/(2) × 800,000. = 400,000 Total money for feeds is Shs. 400,000. Step 2: Calculate the first installment. First installment = 40\% of total feeds money. = 0.40 × 400,000 = 160,000 The first installment is Shs. 160,000. Step 3: Calculate the remainder after the first installment. Remainder after first installment = 400,000 - 160,000. = 240,000 Step 4: Calculate the second installment. Second installment = (2)/(5) of the remainder. = (2)/(5) × 240,000 = 2 × 48,000 = 96,000 The second installment is Shs. 96,000. Step 5: Calculate the third installment. Third installment = Remainder after first installment - Second installment. = 240,000 - 96,000 = 144,000 He will pay Shs. 144,000 for feeds in the third installment. c) The actual PIN the wife will use to withdraw the money. Step 1: Convert the secret number 43 (base 10) to base three. Divide 43 by 3: 43 ÷ 3 = 14 remainder 1 14 ÷ 3 = 4 remainder 2 4 ÷ 3 = 1 remainder 1 1 ÷ 3 = 0 remainder 1 Step 2: Read the remainders from bottom to top. The PIN is 1121_3. The actual PIN the wife will use is 1121. d) The number of days the same feeds will last after buying 100 more chickens. Step 1: Identify the initial conditions. Number of chickens (C_1) = 300. Number of days feeds last (D_1) = 20. Step 2: Identify the new conditions. New number of chickens (C_2) = 300 + 100 = 400. Number of days feeds will last (D_2) = ? Step 3: Apply the inverse proportion relationship. The total amount of feed is constant, so C_1 × D_1 = C_2 × D_2. 300 × 20 = 400 × D_2 6000 = 400 D_2 Step 4: Solve for D_2. D_2 = (6000)/(400) D_2 = 15 The same feeds will last for 15 days after buying 100 more chickens. Send me the next one 📸